Bullock said he is waiting for the contract to arrive at his parents' Grasonville home. Terms of the agreement have not been disclosed.
An All-County and All-Metro selection his senior year at Arundel, Bullock hit .529 with 18 RBI before accepting a full scholarship to Nebraska.
In his sophomore year at Nebraska, the left-hander went 5-5 with a 3.15 earned-run average in less than 100 innings.
"I wasn't expecting to sign this soon, but this has been my goal all along," said Bullock, who will be invited to spring training next year. "I'm really excited about the opportunity."